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 4165

UGCBCS/B.Com/Programme/4th Sem/Comnerce/COMDSC8/av23

UNIVERSITY OF NORTH BENGAL

B.Com. Programme 4th Semester Examination, 2023

DSC8-COMMERCE

BUSINESS MATHEMATICS AND STATISTICS

Time Allotted: 2 Hours Full Marks: 60

The figures in the margin indicate full marks.

GROUP-A/ fs}-$/ qUG-F

Answer any two questions 12x2 = 24

1. (a) The expenditure of 1,000families is given below: 6

Expenditure: 40-59 60-79 80-99 100-119 120-139
No. of Families: 50 500 2 S0
The median of the distribution isRs. 87.50. Find the missing families.
(b) Evaluate: 6

lim x-1

2. (a) Fit astraight line trend equation by the method of least square and estimate the 6
value of 2010:
Year: 2001 2002 2003 2004 2005 2006 2007 2008
Value: 380 400 650 720 690 600 870 930

(b) 1f x =tlogr and y = , find dx at t =1. 6

3. (a) Define Consumer Price Index and explain its uses.

Consurmer Price Index'-44t(e| tg g4K 94 4214f fp
Consumer Price Index yf2414 e VYHol HtMEG EET
(b) Asum of money invested at C. I payable yearly amounts to Rs.
10,816 at the 6
end of the second year and to Rs, 1,248.64 at the end of the third year. Find the
rate of interest and the sum,

4170
Turn Over
 UG/CBCS/B.Com./Programme/44th Sem./Commerce/COMDSC8/2023

StatisicS. 6
marks in Mathematics and
T* (2) Ten students were piven the following
637 148 7
Mathematics (x): 40 20 10 48
3035 25 32 | 1545| 20 3 10 27
Statistics ():
Calculate the rank correlation coefficient between x and y.
2 4
(0) Find the inverse of the matrix A where A=| 5 -2 -3 and hence solve the 6

3 1 6
equation 2x+3y+ 4z=4, 5x- 2y -3z = 4, 3x+ y+6z =1.

GROUP-B/fAs-/qUG-T
5.
Answer any four questions: 6x4=24

(a) Find S.D. from the following

frequency distribution: 6
Weight: 44-46 46-48 48-50 50-52 52-54
Frequency: 3 24 27 21
(b) A function f() is defined as
follows: 6
[3+2x for -3/2sx<0
f(x)=3-2x for 0sx<3/2
-3-2x for x>3/2
Show that f(x) is continuous for x=0 and
discontinuous for x=3/2
(c) Prepare Price Index Number for 2000 with
1994 as base from the following data
by using Fisher's method: 6

1994
Commodity 2000
Quantity| Price (Rs.) Quantity| Price (Rs.)
A 5 2.00
B 2.50 10
4.50
3.20
C 6 8.00 6
4.50
D 2 1.00
1.80
(d) Find frorn the first principle the derivative of
6

(e) Find the matrices Aand B given that:

6
24+B=|[2 3| and 3B-2A 10 17
5 3 5

() Find when:
3+3
(1) y=2.5 (i) 3x'-xy +2y' =0.
2
4170
UG/CBCS/B.Com/Programme/4thSem/Commerce/COMDSC8/2023

GROUP-C/fu-st/qU.
3x4 = 12
questions:
anyfour
Answer
6.

distribution, the Mode and Mean are 32.1 and 35.4 3

asymmetrical
moderately Median,
in a
(a) respectively. Calculatethe 3

is SingularMatrix?
(b) What
Singular Matrixf$p
4-qot oa? 3
SingularMatrix double itselfat 5%
p.a. C. I.?
moneybe 3
a sum of
(c) In what time will
=]x|-2x, find f() and f(-1). 3
(d) If f(*) values ofx and y:
regression find the mean
following lines of
(e) For the 40x-18y = 214 3
&x-10y +66=0, ofx:
68, find the value
the following numbers is
(f) The mean of 26, 81,94.
45, 52, 60, x, 69, 70,

3
4170
 UNIVERSITY OF NORTH BENGAL
B.Com. Honours Part-I Examination, 2019
B.COM.
PAPER-1H2(Revised New Syllabus)
BUSINESS MATHEMATICS AND STATISTICS
Time Allotted: 4 Hours
Full Marks: 100
The figures in the margin indicate full marks.
Candidates are required to give their answers in their own words as far as practicable.
All symbols are of usual significance.
BUSINESs MATHEMATICS
(Marks-50)
GROUP-A
Answer any two questions 15x2 = 30
1. (a) Find the derivative ofy=x from the first principle. 5
ax+b
(b) If f(x)= prove that 5
bx +a

(©) If *"y" =(*+ yy, prove that "= 5

2. (a) Solve, using matrix inverse method

x+2y-z=2
3-4y + 22 =1
-*+3y-z=4

(b) Show that the maximum value of x+- is less than its minimum value. 7

3. (a) Evaluate (any two): 4+4

() *e dt

(b) If.log*_ logy log z prove that x*y'z*-1

y-z *-y

4. (a) If one root of a quadratic equation is square of the other, show that 5
b³ +a'c+ ac² =3abe
Findthe
h) The sum of three numbers in a GP series is 35 and their product is 1000. 5

three number in GP.

1
Turn Over
1030
B.Com./Part-J/Hons./(1+1+1) System/1H2/2019
(c) How many different committees of 7 persons be formed from 8 elected members
and 5 government nominated members in a council.

GROUP-B
5x2 = 10
5. Answer any two questions:
(a) In a class of 100 students, 45 students read Accountancy, 52 students read
Mathematics and 17 students read both the subjects. Find the number of students
who do not read either of the subjects.

(b) Find the middle term in the expansion of

(c) Find the amount of an immediate annuity of Rs. 100 in 10 years allowing 5% p.a.
compound interest.
[Given: (1.05)= 1.629]
(d) Evaluate:
lim M+2x-1-3*

GROUP-C
2x5 = 10
6. Answer any five questions:
(a) If "C, = 2, find the value of n.

(b) Find if x= ct, y=-.

the value of Awhen B= 10.
(C) Avaries inversely as B.IfB=5 then A=4, Find
is and which intersects the
(d) Find the equation of the straight line whose slope 2
origin.
y-axisat a distance of 4 units from the
series
(e) Find the sum of 1st 12terms of the
1215, 405, 135,
() Find if y= 4x +5x+4
and (AnB).
g) Draw Venn Diagram to represent (AUB)
digits can be formed from the nine digits
(h) Find how many different numbers of six
1, 2, 3.........9, ifno digit is repeated.

STATISTICS
(Marks-50)
GROUP-A
Answer any two questions 15x2 =30

x+2y=5, 2x+3y - 8=0. Calculate 5

7. (a) The lines of regression are given by
i) (7,F)
usual meaning.
(ii)'r', where the abbreviations denote the
1030 2
B.Com1Part-/Hons./(1+1+1) System/11H2/2019
(b) Findthe standard deviation of the
Class : 20-29 30-39
following data:
40-49 S0-59 60-69 70-79
Frequency: 5 15 18 80-89
26 16 14 6
(c) Four fair coins are tossed. Find the possibility of
getting exactly two heads.
8. (a) Given:
5
2 4 6 8
y: 5 18 36 59

Applying suitable interpolation formula, estimate the value ofy when x=3.
(b) Calculate the mode of the following data:
Class limits: 130-134 135-139 140-144 145-149 150-154 155-159 160-164
Frequency: 5 15 24 28
17 10 1
(c) The rank correlation co-efficient between the marks in statistics and mathematics 5
obtained by acertain group of students is 0.8. If the sum of the squares of the
differences in ranks is given to be 33, find the number of students in the group.

9. (a) Fora Binomial distribution, mean and sd are 4and W3 respectively. Calculate the 7
probability of getting a non-zero value from this.
(b) How many workers in a factory have a salary between Rs. 400 and Rs. 680 if the
mean salary is Rs. 500 and sd is Rs. 100 and the number of workers is 10000.
(Salary of workers assumed to be normally distributed)
Given: A(1) = 0.3413 A(1.8) =0.4641

5
10.(a) Calculate Fisher's Price Index Number from the given data
Base year Current year
Commodity
Price Quantity Price Quantity
(Kg) (Rs.) (Kg.)
(Rs.)
6
A
6 5
5 10
B
5 10
4 14
C 13
19 2
D 2
5
data:
(b) Obtain the 4-year moving averages for the given 2001 | 2002
1999 2000
1998
1996 1997 18.5 24.5 22.5
Year 16.5
14.5
8.5 12.5
Annual Sales
(Rs. '0000) 5

are its
properties?
(c) Define Poisson Distribution. What
B.Com./Part-VHons./(1+1+1) System/1H2/2019
GROUP-B

11. Answer any two questions: 5x2 =10

(a) The probability that a contractor will get a plumbing contract is 2/3, the
probability that he will not get an electrical contract is 5/9. What is the
probability that he willget both the contracts if the probability of geting at least
one of themis 4/5.
(b) Find the first three central moments of the given frequency distribution
Daily Wages (Rs.): 7-9 9-11 11-13 13-15 15-17 Total
Number of workers: 8 11 18 9 4 50

(c) Find the correlation co-efficient from the following data:

1 3 4 5
6 11 12

(d) The mean annual salary paid to all employees of a company was Rs.
mean annual salaries paid to male and female employees were Rs. 5000. The
5200 and
Rs. 4200 respectively. Find the percentage or % age of male and female
employees in the company.

GROUP-C
12. Answer any five questions: 2x5 = 10
(a) What is the relation between Mean, Median and Mode?
(b) The sd of 32 observations is 5. If the sum of these observations is 80, find the
sum of squares of the observations.
(c) Given =36, Y=44, XY = 24, find 'r".
(a) What is the probability of getting a king in a draw of one card from a pack of 52
cards?
(e) From the following data, calculate price index using simple aggregative method
Price (Rs.)
Item 2011 2016
A 32 48
B 16 28
12 24

(f) If o, =4, o, = 5, cor(x, y) =8 , find the value of byg.

(g) If r =0.6, cor(x, y) =12, a5, find a.
(h) Find median and mode of the following:
40, 36, 37, 32, 33, 33, 35, 32, 40,42.

1030 4